Patients receive cetuximab intravenously (IV) over 60 minutes, paclitaxel IV over 1 hour, and carboplatin IV over 30 minutes on day 1. Beginning in course 2, patients also receive erlotinib hydrochloride orally (PO) once daily (QD) on days 1-21. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity.